Here are two icosahedral pencil holders.
They were constructed by replacing the triangular faces of an icosahedron with triangular motifs like those in thing 75045 - Desk Ornaments. The topmost face of the icosahedron was deleted and a prism added to the base.
Stl files are:
and the openSCAD code is: icosa_holder.scad.
Both files can be printed directly on the build surface. Nice prints were produced by my Replicator without the need for support. I used two shells, 10% infill and the prints weighed about 25 grams.